The relation between the mean and variance of chisquare with n d.f. is: *
Answers
The distribution of the chi-square statistic is called the chi-square distribution. In this lesson, we learn to compute the chi-square statistic and find the probability associated with the statistic. And we'll work through some chi-square examples to illustrate key points.
The Chi-Square Statistic
Suppose we conduct the following statistical experiment. We select a random sample of size n from a normal population, having a standard deviation equal to σ. We find that the standard deviation in our sample is equal to s. Given these data, we can define a statistic, called chi-square, using the following equation:
Χ2 = [ ( n - 1 ) * s2 ] / σ2
The distribution of the chi-square statistic is called the chi-square distribution. The chi-square distribution is defined by the following probability density function:
Y = Y0 * ( Χ2 ) ( v/2 - 1 ) * e-Χ2 / 2
where Y0 is a constant that depends on the number of degrees of freedom, Χ2 is the chi-square statistic, v = n - 1 is the number of degrees of freedom, and e is a constant equal to the base of the natural logarithm system (approximately 2.71828). Y0 is defined, so that the area under the chi-square curve is equal to one.
Answer:
The Chi - square distribution has the following properties : The mean of the distribution is equal to the number of degrees of freedom :ų=v